function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%
%size( nn_params )
% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

%size( Theta1 )
%size( Theta2 )

% Setup some useful variables
m = size(X, 1);
         
% You need to return the following variables correctly 
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a 
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the 
%               first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%
%m
% size( X ) 5000 400
%size( Theta1 ) %25 401
%size( Theta2 ) %10 26

a1 = [ones(m, 1) X]; % 5000 401
z2 = a1 * Theta1'; % 5000 25
a2 = sigmoid( z2 );
a2 = [ones(m, 1) a2]; % 5000 26
z3 = a2 * Theta2';
a3 = sigmoid( z3 ); % 5000 10

Y = eye( num_labels ) ( y, : ); % 5000 10
%Y = zeros( m, num_labels );
%for i = 1:m
%	Y( i, y( i ) ) = 1;
%end

J = -sum( sum( Y .* log( a3 ) + ( 1 - Y ) .* log( 1 - a3 ) ) ) / m;
R = lambda * ( sum( sum( Theta1( :, 2:end ) .^2 ) ) + sum( sum( Theta2( :, 2:end ) .^2 ) ) ) / ( 2 * m );
J = J + R;

delta3 = a3 .- Y; % 5000 10
%size( delta3 )

%tempTheta2 = Theta2( :, 2:end );
%size( tempTheta2 )
%size( z2 )
%size( Theta2' * delta3 )
%delta2 = ( Theta2' * delta3 );
%delta2 = delta2 .* sigmoidGradient( z2 );
delta2 = ( delta3 * Theta2 )( :, 2:end ) .* sigmoidGradient( z2 ); % 5000 25
D1 = delta2' * a1;
D2 = delta3' * a2;
%size( D1 ) % 25 401
%size( D2 ) % 10 25
D1( :, 2:end ) = D1( :, 2:end ) .+ lambda * Theta1( :, 2:end );
D2( :, 2:end ) = D2( :, 2:end ) .+ lambda * Theta2( :, 2:end );

Theta1_grad = D1 / m ;
Theta2_grad = D2 / m;
%Theta2_grad( :, 2:end ) = Theta2_grad( :, 2:end ) .+ lambda * Theta2( :, 2:end );
%size( Theta1_grad ) % 25 401
%size( Theta2_grad ) % 10 25



%size( delta3 )
%size( a2 )
%size( delta2 )
%size( X )









% -------------------------------------------------------------

% =========================================================================
%size( Theta1_grad )
%size( Theta2_grad )
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];
%size( grad )

end
